Thermally and chemically reacted MHD Maxwell nanofluid flow past an inclined permeable stretching surface

2021 ◽  
pp. 095440892110507
Author(s):  
Amar B. Patil ◽  
Vishwambhar S. Patil ◽  
Pooja P. Humane ◽  
Nalini S. Patil ◽  
Govind R. Rajput
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Similarity Transformations ◽  
Flow Past ◽  
Chemically Reacting ◽  
The Impact

The present work deals with chemically reacting unsteady magnetohydrodynamic Maxwell nanofluid flow past an inclined permeable stretching surface embedded in a porous medium with thermal radiation. The formulated governing partial differential equations conveying the flow model of Maxwell with Buongiorno modeled nanofluid is transformed into the system of highly non-linear ordinary differential equations via suitable similarity transformations; those equations are transmuted into an initial value problem and then solved numerically by a shooting approach with Runge–-Kutta fourth-order schema. To obtain the physical insight of the flow situation, the influence of associated parameters on the velocity, temperature, and concentration profiles is sketched graphically with the aid of MATLAB software. Furthermore, engineering quantities of interest are interpreted graphically. The computed numerical results are compared to estimate the validity of the achieved results; it has been found out that the computed results are highly accurate. The impact of the Maxwell parameter and inclination angle of the sheet on the velocity field is observed in decaying. Both thermal and solutal energy transport are progressive in nature as the Maxwell parameter and thermophoresis parameter grows, and a reverse trend is observed for Prandtl number.

scholarly journals A Numerical Approach for an Unsteady Tangent Hyperbolic Nanofluid Flow past a Wedge in the Presence of Suction/Injection

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
U. Shahzad ◽  
M. Mushtaq ◽  
S. Farid ◽  
K. Jabeen ◽  
R.M.A. Muntazir
Keyword(s):  
Differential Equations ◽  
Graphical Representation ◽  
Numerical Technique ◽  
Darcy Number ◽  
Numerical Approach ◽  
Nanofluid Flow ◽  
Similarity Transformations ◽  
Flow Past ◽  
Layer Flow ◽  
The Impact

The analysis of unsteady tangent hyperbolic nanofluid flow past a wedge with injection-suction, because of its beneficial uses, has gained a lot of attention. The present study is mainly concerned with tangent hyperbolic nanofluid (non-Newtonian nanofluid). First, we have converted the system of partial differential equations (PDEs) to a system of ordinary differential equations (ODEs) with the help of appropriate similarity transformations. Boundary conditions are also transformed by utilizing suitable similarity transformation. Now, for the obtained ODEs, we have used the numerical technique bvp 4 c and investigated the velocity, temperature, and concentration profiles. The accuracy of the flow model is validated by applying MAPLE d-solve command having good agreement while comparing the numerical results obtained by bvp4c for both suction and injection cases. The effects of distinct dimensionless parameters on the various profiles are being analyzed. The novel features such as thermophoresis and Brownian motion are also discussed to investigate the characteristics of heat and mass transfer. Graphical representation of the impact of varying parameters and the solution method for the abovementioned model is thoroughly discussed. It was observed that suction or injection can play a key role in controlling boundary layer flow and brings stability in the flow. It was also noticed that by increasing the Darcy number, velocity profile increases in both injection-suction cases.

scholarly journals Numerical Simulation of Heat Mass Transfer Effects on MHD Flow of Williamson Nanofluid by a Stretching Surface with Thermal Conductivity and Variable Thickness

Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 684
Author(s):  
Saeed Islam ◽  
Haroon Ur Rasheed ◽  
Kottakkaran Sooppy Nisar ◽  
Nawal A. Alshehri ◽  
Mohammed Zakarya
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Variable Thickness ◽  
Heat Mass Transfer ◽  
Mathematical Formulation ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
The Impact

The current analysis deals with radiative aspects of magnetohydrodynamic boundary layer flow with heat mass transfer features on electrically conductive Williamson nanofluid by a stretching surface. The impact of variable thickness and thermal conductivity characteristics in view of melting heat flow are examined. The mathematical formulation of Williamson nanofluid flow is based on boundary layer theory pioneered by Prandtl. The boundary layer nanofluid flow idea yields a constitutive flow laws of partial differential equations (PDEs) are made dimensionless and then reduce to ordinary nonlinear differential equations (ODEs) versus transformation technique. A built-in numerical algorithm bvp4c in Mathematica software is employed for nonlinear systems computation. Considerable features of dimensionless parameters are reviewed via graphical description. A comparison with another homotopic approach (HAM) as a limiting case and an excellent agreement perceived.

Radiation and Partial Slip Effects on Magnetohydrodynamic Jeffrey Nanofluid Containing Gyrotactic Microorganisms Over a Stretching Surface

2020 ◽  
Vol 13 (3) ◽  
Author(s):  
K. Kumaraswamy Naidu ◽  
D. Harish Babu ◽  
S. Harinath Reddy ◽  
P. V. Satya Narayana
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Coupled System ◽  
Partial Slip ◽  
Stretching Surface ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Jeffrey Nanofluid ◽  
The Impact

Abstract In this study, the impact of thermal radiation and partial slip on magnetohydrodynamic flow of the Jeffrey nanofluid comprising motile gyrotactic microorganisms via vertical stretching surface is analyzed. The governing partial differential equations are reformed to a system of coupled ordinary differential equations by utilizing the similarity transformations. The transformed equations are of order four, which are complex to solve analytically and hence, the coupled system is solved computationally by using the shooting technique along the Runge–Kutta integrated scheme. The ramifications of different thermophysical parameters on the density of gyrotactic microorganisms, Jeffrey nanofluid velocity, nanoparticles concentration, temperature, Sherwood number, and Nusselt number are illustrated graphically. Comparing this study with the results already published favors the validity of this study. It is established that the Nusselt number is boosted on enhancing the thermal radiation parameter, and the reverse trend has been observed on increasing the Richardson number, whereas the gyrotactic microorganisms density is more in case of viscous nanofluid compared to the Jeffrey nanofluid.

Mixed convective 3D flow of Maxwell nanofluid induced by stretching sheet: Application of Cattaneo-Christov theory

2020 ◽  
pp. 095440622097324
Author(s):  
Awais Ahmed ◽  
Masood Khan ◽  
Jawad Ahmed ◽  
Asia Anjum ◽  
Sohail Nadeem
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Sheet ◽  
Thermal Relaxation ◽  
Maxwell Fluid ◽  
Brownian Diffusion ◽  
Flow Mechanism ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Text Component

The present study invokes the application of Cattaneo-Christov theory for the thermal analysis in the buoyancy driven three dimensional flow of Maxwell nanofluid. The flow is induced above the vertical bidirectional stretching sheet. The phenomena of thermophoresis and Brownian diffusion of nanoparticles in the flow Maxwell liquid are deliberated with the help of Buongiorno model for nanofluid. The physical problem is formulated in the form of boundary layer partial differential equations (PDEs). Moreover, suitable ansatz for flow mechanism are employed to reduce the governing PDEs into the non-linear ordinary differential equations (ODEs). The flow mechanism of Maxwell fluid along with energy transport is analyzed in the form of homotopic solutions of the governing ODEs. The outcomes are presented graphically and discussed with physical explanation. The analysis revealed that both buoyancy and mixed convection parameters enhanced the [Formula: see text]-component of velocity field but declined the [Formula: see text]-component. Moreover, in assisting mode these two parameters also increased the thermal and solutal energy transport in nanofluid. It is noted that the thermophorectic force boosts up the thermal energy transport in the flow in the presence of thermal relaxation phenomenon. The validation of the present results are confirmed through tabular data with some previous studies.

scholarly journals Numerical study of chemically reacting unsteady Casson fluid flow past a stretching surface with cross diffusion and thermal radiation

2017 ◽  
Vol 7 (1) ◽  
pp. 69-76 ◽  
Author(s):  
K. Pushpalatha ◽  
J.V. Ramana Reddy ◽  
V. Sugunamma ◽  
N. Sandeep
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Casson Fluid ◽  
Stretching Surface ◽  
Cross Diffusion ◽  
Similarity Transformations ◽  
Chemically Reacting ◽  
Fourth Order Method

AbstractThe problem of an unsteady MHD Casson fluid flow towards a stretching surface with cross diffusion effects is considered. The governing partial differential equations are converted into a set of nonlinear coupled ordinary differential equations with the help of suitable similarity transformations. Further, these equations have been solved numerically by using Runge-Kutta fourth order method along with shooting technique. Finally, we studied the influence of various non-dimensional governing parameters on the flow field through graphs and tables. Results indicate that Dufour and Soret numbers have tendency to enhance the fluid velocity. It is also found that Soret number enhances the heat transfer rate where as an opposite result is observed with Casson parameter. A comparison of the present results with the previous literature is also tabulated to show the accuracy of the results.

scholarly journals A Framework for the Magnetic Dipole Effect on the Thixotropic Nanofluid Flow Past a Continuous Curved Stretched Surface

Crystals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 645
Author(s):  
Noor Saeed Khan ◽  
Auwalu Hamisu Usman ◽  
Arif Sohail ◽  
Abid Hussanan ◽  
Qayyum Shah ◽  
...  
Keyword(s):  
Magnetic Dipole ◽  
Radiation Effects ◽  
Analysis Method ◽  
Governing Equations ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Nanoparticles Concentration

The magnetic dipole effect for thixotropic nanofluid with heat and mass transfer, as well as microorganism concentration past through a curved stretching surface, is discussed. The flow is in a porous medium, which describes the Darcy–Forchheimer model. Through similarity transformations, the governing equations of the problem are transformed into non-linear ordinary differential equations, which are then processed using an efficient and powerful method known as the homotopy analysis method. All the embedded parameters are considered when analyzing the problem through solution. The dipole and porosity effects reduce the velocity, while the thixotropic nanofluid parameter increases the velocity. Through the dipole and radiation effects, the temperature is enhanced. The nanoparticles concentration increases as the Biot number and curvature, solutal, chemical reaction parameters increase, while it decreases with increasing Schmdt number. The microorganism motile density decreases as the Peclet and Lewis numbers increase. Streamlines demonstrate that the trapping on the curved stretched surface is uniform.

scholarly journals Convective Heat Transfer of a Hybrid Nanofluid over a Nonlinearly Stretching Surface with Radiation Effect

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2220
Author(s):  
Emad H. Aly ◽  
Alin V. Roşca ◽  
Natalia C. Roşca ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Radiation Effect ◽  
Numerical Technique ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Temperature Parameter ◽  
Nonlinearly Stretching Surface

The flow of the hybrid nanofluid (copper–titanium dioxide/water) over a nonlinearly stretching surface was studied with suction and radiation effect. The governing partial differential equations were then converted into non-linear ordinary differential equations by using proper similarity transformations. Therefore, these equations were solved by applying a numerical technique, namely Chebyshev pseudo spectral differentiation matrix. The results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that the rising of the mass flux parameter slows down the velocity and, hence, decreases the temperature. Further, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, it was mentioned that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases.

Fluid relaxation and retardation time properties in the flow of Burgers fluid subject to modified heat and mass flux theory

2021 ◽  
pp. 095440892110670
Author(s):  
Zahoor Iqbal ◽  
Awais Ahmed ◽  
Amina Anwar ◽  
Sivanandam Sivasankaran ◽  
Ali Saleh Alshomrani ◽  
...  
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Flow Problem ◽  
Fluid Motion ◽  
Retardation Time ◽  
Linear Ordinary Differential Equations ◽  
Fluid Parameter ◽  
Burgers Fluid ◽  
Time Parameters ◽  
The Impact

In this study, the heat transport is scrutinized in the flow of magnetized Burgers fluid accelerated by stretching cylinder. Rather than, classical Fourier's and Fick's laws, the Cattaneo-Christov theory featuring the improved heat and mass conduction is utilized to investigate the energy transport. Further, the transport of thermal and solutal energy is controlled by the significant influence of heat generation/absorption and chemical reaction. The physical flow problem is modelled in the form of partial differential equations (PDEs) which are then transformed into the non-linear ordinary differential equations (ODEs) by invoking appropriate similarity variables. The numerical simulation to the system of ODE's is tackled by employing BVP-Midrich scheme in Maple. The numerical results for flow field, thermal and concentration distributions are exhibited graphically. The impact of fluid relaxation and retardation time parameters on the velocity field are observed in growing and decaying way, respectively. Both the thermal and solutal energy transport decline with higher values of retardation time parameter. The rise in Burgers fluid parameter enhances the transport of energy during the fluid motion. The effect of thermal and solutal relaxation time parameters on heat and mass transport in the fluid are noticed in the declining manner.

Forced convection in 3D Maxwell nanofluid flow via Cattaneo–Christov theory with Joule heating

2021 ◽  
pp. 095440892199963
Author(s):  
Awais Ahmed ◽  
Masood Khan ◽  
Mahnoor Sarfraz ◽  
Jawad Ahmed ◽  
Zahoor Iqbal
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Joule Heating ◽  
Energy Transport ◽  
Fluid Motion ◽  
Analytical Technique ◽  
Maxwell Nanofluid ◽  
Homotopy Analysis ◽  
Non Linear System ◽  
The Impact

In this article, an investigation of the thermal and solutal energy transport in the 3 D flow of Maxwell nanofluid through a porous medium under the influence of the magnetic field is performed. The heat generation source and chemical reaction are also taken in account as a controlling agent for the heat and mass transport in the Maxwell liquid. A novel idea of Cattaneo-Christov theory and Buongiorno model for nanofluid is employed under the impact of Joule heating for the present analysis. The governing partial differential equations (PDEs) are transformed into a non-linear system of ordinary differential equations (ODEs) by using flow similarities. The solution of similar ODEs is constructed through a well known semi-analytical technique which is the homotopy analysis method. The results of the investigation are explored in the form of graphs. It is observed that higher values of magnetic field decline the flow field. The temperature and concentration distributions decrease with the higher magnitude of thermal and solutal relaxation time phenomena, respectively. Moreover, the temperature field enhances when the Brownian motion of nanoparticles increases in flow while the concentration profile decreases. Also, it is found that the increase in resistive heating boosts up the thermal energy transport in the fluid motion.

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